Silica-Assisted Nucleation of Polymer Foam Cells with Nanoscopic Dimensions: Impact of Particle Size, Line Tension, and Surface Functionality.

Core-shell nanoparticles consisting of silica as core and surface-grafted poly(dimethylsiloxane) (PDMS) as shell with different diameters were prepared and used as heterogeneous nucleation agents to obtain CO2-blown poly(methyl methacrylate) (PMMA) nanocomposite foams. PDMS was selected as the shell material as it possesses a low surface energy and high CO2-philicity. The successful synthesis of core-shell nanoparticles was confirmed by Fourier transform infrared spectroscopy, thermogravimetric analysis, and transmission electron microscopy. The cell size and cell density of the PMMA micro- and nanocellular materials were determined by scanning electron microscopy. The cell nucleation efficiency using core-shell nanoparticles was significantly enhanced when compared to that of unmodified silica. The highest nucleation efficiency observed had a value of ∼0.5 for nanoparticles with a core diameter of 80 nm. The particle size dependence of cell nucleation efficiency is discussed taking into account line tension effects. Complete engulfment by the polymer matrix of particles with a core diameter below 40 nm at the cell wall interface was observed corresponding to line tension values of approximately 0.42 nN. This line tension significantly increases the energy barrier of heterogeneous nucleation and thus reduces the nucleation efficiency. The increase of the CO2 saturation pressure to 300 bar prior to batch foaming resulted in an increased line tension length. We observed a decrease of the heterogeneous nucleation efficiency for foaming after saturation with CO2 at 300 bar, which we attribute to homogenous nucleation becoming more favorable at the expense of heterogeneous nucleation in this case. Overall, it is shown that the contribution of line tension to the free energy barrier of heterogeneous foam cell nucleation must be considered to understand foaming of viscoelastic materials. This finding emphasizes the need for new strategies including the use of designer nucleating particles to enhance the foam cell nucleation efficiency.

Introduction

Polymer foams are materials with numerous applications and are used, for example, as energy absorbing systems, in thermal insulation, and as catalyst carriers.[1−3] When the cell size in closed cell foams is smaller than the collision mean free path of the encapsulated gas molecules (∼70 nm at room temperature and at an absolute pressure of 1 atm), the collisions between gas molecules are reduced and as a consequence the thermal conduction by the gas phase enclosed in the foam cells is significantly decreased. This is referred to as the so-called Knudsen effect.[4,5] This makes nanocellular polymer foams very promising candidates as high-performance thermal insulation materials.[2] However, the fabrication of foams with such small cells and with high cell densities remains a scientific and technological challenge.[2,3]

Among the possible foaming strategies, CO2 batch foaming holds great promise to prepare nanocellular foams.[6−14] This is due to the easy control of the foaming conditions and the use of CO2 as an environmentally benign blowing agent. Disadvantages of batch foaming include that (i) it is limited to relatively small specimen sizes and (ii) it has a lower production efficiency when compared to that of continuous processes.

Tuning the foam cell morphology, defined by the cell size, cell density, cell size distribution, and cell structure (e.g., open or closed cells), is an issue of great practical interest that will eventually allow one to determine the optimum foam structure for the targeted application.[15,16] For instance, polymer foams with cell sizes of 100 nm or less and a cell density of 1015–1016 cells cm–3 show a high thermal insulation performance, which is ascribed to the already introduced Knudsen effect.[3] However, nanocellular polymer foams with small cell sizes (<100 nm) and with high cell densities (>1015 cells cm–3) are still rarely reported.[17−19] Besides optimization of the foaming conditions, another common strategy to enhance cell morphology control is to introduce nanostructured heterogeneous phases to the foamed matrix to act as heterogeneous nucleation sites during foaming.[2,12] In general, according to the classical nucleation theory, heterogeneous cell nucleation would be preferable due to lower nucleation energy barriers when compared with homogeneous nucleation.[20] For instance, (nano)particulate fillers[17,21−29] and block (co)polymers[30−33] have been reported in the open literature as heterogeneous nucleation agents.

Silica nanoparticles are of particular interest as heterogeneous nucleation agents in polymer foaming due to their low cost, easy preparation, good size control, and the ease of employing various surface functionalization strategies for their surface decoration. For instance, He and co-workers[24] reported that the addition of silica nanoparticles in polycarbonate prior to foaming resulted in a more uniform cell size distribution and higher cell density due to heterogeneous nucleation compared to those in the pristine polycarbonate foams. Spontak and co-workers[10] described the influence of nanoparticle concentration on cell morphology in CO2-assisted PMMA foaming. The authors demonstrated that below a certain concentration of the nucleating silica nanoparticles the cell size decreases and the cell density increases with increasing particle concentration. Zhong and co-workers[34] as well as Ozisik and co-workers[27] have demonstrated that the surface derivatization of silica nanoparticles with CO2-philic surfactants can decrease the nucleation energy and significantly enhance the cell nucleation efficiency in CO2 polymer foaming compared to those in pristine particles. The nucleation efficiency is defined as the ratio of the number of cells per cm3 unfoamed material to the number of nanoparticles per cm3 added to the polymer before foaming.[13,35] In addition, we recently reported the synthesis of PDMS-grafted silica nanoparticles with a core diameter of 80 nm as highly efficient cell nucleation agents in CO2-blown batch foaming of polystyrene and poly(methyl methacrylate) films.[13] Nucleation efficiencies of up to ∼0.5 (i.e., 1 foam cell per 2 particles on average) were achieved for the foaming conditions we reported. This is the highest nucleation efficiency value observed so far for nanoparticles used as heterogeneous nucleation agents. We note that in this work we used a custom-build batch foaming device that allows the saturation of polymers with CO2 at pressures up to 300 bar (for further details, see Figure S1).

To obtain nanocellular materials in a robust and controlled way, we embarked on a study of the influence of interfacial interactions and particle curvature on cell nucleation. To this end, in this work, bare SiO2 nanoparticles with surface-exposed silanol groups and PDMS-grafted core–shell nanoparticles (SiO2-PDMS) with different silica core diameters (from 12 to 120 nm) were prepared and subsequently incorporated in PMMA to function as heterogeneous nucleation agents. We selected a CO2 saturation pressure of 55 bar and a foaming temperature of 40 °C on the basis of our previously reported results as this ensures highly efficient foam cell nucleation by PDMS-grafted core–shell nanoparticles.[13] Under these conditions, heterogeneous nucleation is still favorable compared with homogenous nucleation, and the effect of particle size and surface chemistry is thus expected to determine the foam morphologies. In addition, this pressure (i.e., 55 bar) is significantly lower than pressures used during the frequently exploited supercritical foaming conditions in batch foaming, for example, using pressures up to 330 bar.[36,37] We expect that an enhanced understanding of heterogeneous nucleation and foaming at relatively low saturation pressures would eventually result in the development of industrially relevant foaming processes.

We considered it of particular interest to decrease the PDMS-grafted core–shell particle size to below the earlier reported silica core diameter of 80 nm[13] because a decreased particle size allows one to introduce more foam cell nucleation sites, whereas the weight percentage of particle loading is kept constant. Provided that smaller particles nucleate foam cells as efficiently as larger ones, the use of smaller particles is expected to yield foams with a higher cell density and a lower overall foam density. Foams for thermal insulation applications are expected to benefit from as low as possible silica weight concentrations also since silica is a good thermal conductor. As we show later, nanoparticles with a high surface curvature, that is, small diameters, especially below 40 nm, were found to be less efficient for heterogeneous nucleation compared with particles with a larger size. We report here that the less efficient nucleation for the smaller particles is ascribed to positive line tension values acting at the three-phase contact line among the nanoparticle, CO2 nucleus, and CO2 swollen polymer. Line tension is defined as the excess free energy per unit length of a contact line where three distinct phases coexist.[38] Although the length scale over which line tension effects become relevant for viscoelastic polymer/particle systems in foaming is not yet fully understood, it is generally accepted that line tension effects become significant at diminishing dimensions.[39−41] In fact, we show explicitly that at the length scales relevant for our foaming process, line tension must be included in the models for quantitatively describing the free energy of cell nucleation in polymer foaming.

Interestingly, morphology imaging of cellular materials, and in particular, capturing the position of the nucleating particles with respect to the matrix–cell gas interface, provides information about the influence of line tension effects on cell nucleation. For example, scanning electron microscopy (SEM) micrographs reveal the absence of the smallest nanoparticles at the surface of the foam cell walls. This observation supports the significance of a positive line tension and thus confirms that its contribution to the free energy of cell nucleation must be included in the models describing foaming. These results further underline the importance of obtaining an enhanced understanding of the interactions between highly curved particles with viscoelastic polymers when particle sizes are at the nanometer length scale. Related knowledge would allow one to fully exploit the potential of nanoparticles as highly efficient nucleation agents in nanocellular foaming, as well as line tension effects in numerous other applications, such as in electronics,[42] sensors,[43,44] adhesives,[45] and templated porous materials.[46]

Materials and Methods

Materials

Tetraethyl orthosilicate (TEOS) ≥ 99.0% and 2-propanol 99.5% were purchased from Aldrich (Milwaukee, WI). (3-Aminopropyl)-triethoxysilane (APTES) 99%, hydrochloric acid 37%, and ammonium hydroxide solution 28–30% were purchased from Sigma-Aldrich (St. Louis, MO). Monoglycidyl ether-terminated poly(dimethylsiloxane) (PDMS-G) (Mw = 1000 and 5000 g mol–1) was purchased from Gelest (Morrisville, PA). N-(2-aminoethyl-3-aminopropyl)methyldimethoxysilane (Dynasylan 1411) ≥ 99.0% was obtained from Evonik (Marl, Germany). PMMA granules were acquired from Arkema (VM100, i.e., a PMMA-co-EA polymer, ρ = 1.18 g cm–3) (La Garenne-Colombes, France). Nanoparticles with diameters of 12 nm (Bindzil 40/220), 20 nm (Bindzil 40/130), and 60 nm (Levasil 50/50) were a gift from AkzoNobel (Bohus, Sweden). These particles were dispersed in aqueous solution and have surface-exposed silanol groups on the surface as received. Absolute tetrahydrofuran (THF) was purchased from Biosolve (Valkenswaard, The Netherlands). Ethanol absolute for analysis was obtained from Merck (Darmstadt, Germany). Milli-Q water was produced by a Millipore Synergy system (Billerica, MA). Unless otherwise mentioned, all other chemicals were used as received.

Nanoparticle Synthesis

Stöber Silica Nanoparticle Preparation

To prepare nanoparticles (SiO2) using the Stöber method (hereinafter we abbreviate “nanoparticle” with NP) with a diameter of ∼80 nm, 168 mL of ethanol was mixed with 28 mL of Milli-Q water and 30 mL of TEOS in the presence of 2 mL of ammonium hydroxide while stirring at 500 rpm at room temperature. After 1.5 h, the obtained SiO2 dispersion was centrifuged at 10 000 rpm for 30 min. Subsequently, the collected SiO2 was redispersed in ethanol and centrifuged again. This washing step was repeated 2 more times, followed by vacuum-drying the collected SiO2 NPs at room temperature for 12 h. To synthesize the 40 nm particles, 84 mL of ethanol was mixed with 14 mL of Milli-Q water and 15 mL of TEOS in the presence of 0.75 mL of ammonium hydroxide in a 250 mL round bottom flask while stirring at 500 rpm. The reaction was conducted for 1.5 h at room temperature. To obtain the 120 nm particles, 100 mL of ethanol was mixed with 8 mL of Milli-Q water and 5 mL of TEOS in a round bottom flask stirring at 500 rpm and subsequently 5 mL of ammonium hydroxide was added and reacted for 3 h at 50 °C. The collecting, washing, and drying steps of these NPs were the same as those described for NPs of 80 nm.

Hydrolysis

To introduce silanol groups on the surface of the SiO2 NPs, the particles were redispersed in Milli-Q water by sonication (BRANSON 2510, Canada) for 1 h. Subsequently, hydrochloric acid was added to the dispersion while stirring at 500 rpm until the pH of the solution reached a value of approximately 1. After 4 h, the dispersion was centrifuged at 10 000 rpm for 30 min. The collected NPs were redispersed in Milli-Q water and centrifuged again. This washing step was repeated 2 more times, followed by drying the silanol functional NPs (SiO2-OH) in vacuum at room temperature for 12 h.

Amino-Functionalization

SiO2-OH NPs (3.0 g) were redispersed in 100 mL of ethanol, followed by the addition of 15 mL of APTES. The dispersion was left to stir at 500 rpm at room temperature for 17 h. The APTES-functionalized NPs (SiO2-NH2) were collected by centrifugation at 10 000 rpm for 30 min, redispersed in ethanol, and centrifuged again. This washing step was repeated 2 more times, followed by drying the collected SiO2-NH2 NPs in vacuum at room temperature for 12 h.

The Bindzil 40/220, Bindzil 40/130, and Levasil 50/50 particles with diameters of 12, 20, and 60 nm, respectively, were functionalized with Dynasylan 1411 to render their surface to exhibit amino-functionality. In a typical procedure, 7 mL of Dynasylan 1411 was added to 10 mL of NP suspension. The dispersion was left to stir at 500 rpm at room temperature for 17 h. The amino-functionalized NPs (SiO2-NH2) with diameters of 12 and 20 nm were collected by the addition of 5 mL of calcium chloride (1 mol L–1) that induces reversible aggregation of the NPs, followed by centrifugation at 10 000 rpm for 30 min. The reversible NP aggregation aids in their sedimentation during centrifugation. The particles were subsequently redispersed in ethanol. This washing step was repeated 2 more times, followed by drying the collected SiO2-NH2 NPs in vacuum at room temperature for 12 h. The Levasil 50/50 NPs were collected by repeated centrifugation as described earlier.

Grafting to of PDMS-G to Silica NPs

SiO2-NH2 NPs (1.0 g) were redispersed in 20.5 mL of THF and 15 g of PDMS-G while stirring at 500 rpm for 1 hour, followed by sonication for 1 h. Subsequently, THF was removed by rotary evaporation and the resulting silica NP dispersion in PDMS-G was immersed in an oil bath, thermostated at 80 °C for 17 h. Following cooling to room temperature, the reaction mixture was washed with THF and centrifuged at 10 000 rpm for 30 min. This washing step was repeated 2 more times, followed by vacuum-drying the SiO2-PDMS at room temperature for 12 h.

Nanocomposite Film Preparation

Nanocomposites were prepared by dispersing an amount of (functional) silica NPs (2.3 × 1013 cm–3) in PMMA with a mini extruder (DSM Xplore, The Netherlands). The number density of NPs was kept constant at the value mentioned throughout this study. In a typical procedure, a dry blend of NPs and PMMA was fed to the extruder, followed by internal mixing for 3 min. The barrel temperature was set to 155 °C, and the screw speed was 100 rpm. Subsequently, the PMMA nanocomposite was collected and left to cool to room temperature.

Film Preparation

A hot press (Fontijne, The Netherlands) was used to press ∼0.2 mm thick nanocomposite films in a mold (4 × 3 cm2). The press temperature, applied load, and press time were 180 °C, 250 kN, and 10 min, respectively.

Batch Foaming of Nanocomposite Films

The nanocomposite PMMA films were saturated with CO2 (55 bar) in an autoclave for 4 h at room temperature, followed by rapid depressurization. Subsequently, the PMMA nanocomposite films were immersed in a water bath thermostated at 40 °C for different foaming times (0.3 and 180 s), after which the samples were quenched in an ice bath for 30 min. The samples were left to dry in air for at least 12 h prior to further analysis. For a scheme of the custom-built foaming setup we used, see Figure S1.

Characterization

Fourier Transform Infrared (FTIR) Spectroscopy

FTIR spectra were collected with a Bruker α single attenuated total reflection (ATR) FTIR Spectrometer equipped with an ATR single-reflection crystal (Bruker Optic GmbH, Ettlingen, Germany). The spectra were collected in the range of 4000–400 cm–1 (spectral solution of 4 cm–1, 128 scans). Background spectra were recorded against air.

Thermogravimetric Analysis (TGA)

The weight loss of the (modified) particles as a function of temperature was measured with a TGA400 (PerkinElmer, Inc., Waltham, MA). A sample weighing ∼5–10 mg was loaded into a platinum pan, and the temperature was set to 50 °C to stabilize. Subsequently, the sample was heated to 900 °C at a heating rate of 20 °C min–1. The applied air flow was 20 mL min–1.

Transmission Electron Microscopy (TEM)

The core–shell structure of the functionalized NPs was visualized by a FEI/Philips CM300 transmission electron microscope (Eindhoven, The Netherlands). For TEM imaging, diluted particle dispersions in THF were deposited on the carbon side of a carbon/copper grid (HC200-Cu) (EMS, Germany). Images were obtained in the bright field mode with a 300 kV acceleration voltage.

Scanning Electron Microscopy (SEM)

To investigate the cellular morphology of the foamed nanocomposite films, a high-resolution scanning electron microscope (JEOL Field Emission JSM-633OF, JEOL Benelux, Nieuw-Vennep, The Netherlands) was utilized. The typically used electron acceleration voltage was 5 keV. Prior to analysis, the nanocomposite foams were freeze-fractured after cooling in liquid nitrogen for 10 min.

Calculation of Cell Density and Nucleation Efficiency

The cell size and cell density were obtained by analyzing the SEM cross-sectional images. The cell density (Nv) of the foams was calculated according to Kumar’s theoretical approximation.[47] No direct measurements of cell dimensions are required in this method; only the micrograph area (A) and the total number of cells (n) contained therein should be determined. Together with the magnification factor of the micrograph (M), Nv can be calculated according to eq .By combining Nv with the volume expansion ratio (B) (i.e., the ratio of the PMMA film volume after foaming to its volume before foaming) of nanocomposite films after foaming (see Table S3), the cell number per cm3 of unfoamed materials (N) can be calculated according to eq .Cell density values mentioned further in this study refer to N.

In addition, the nucleation efficiency (f) of NPs during foaming can be calculated aswhere C is the number of NPs per cm3 (i.e., 2.3 × 1013) added to the polymer during melt blending.[13] We have observed a homogenous particle distribution by cross-sectional SEM imaging of polymer nanocomposite films prior to foaming.

Results and Discussion

Preparation and Characterization of Silica NPs

Stöber silica NPs with different diameters were synthesized, followed by their surface grafting with PDMS. The reaction scheme of the process we used is depicted in Figure A. Typically, silica NPs (SiO2) were prepared via a Stöber reaction[48] (step a), followed by the hydrolysis of the surface-exposed ethoxy groups to silanol moieties (step b). The hydrolyzed particles (SiO2-OH) were derivatized with (3-aminopropyl)-triethoxysilane (APTES), resulting in the formation of amine-functionalized NPs (SiO2-NH2) (step c). Subsequently, PDMS-grafted core–shell NPs (SiO2-PDMS) were prepared by the “grafting to” method using monoglycidyl ether-terminated PDMS (step d). When commercially available silica core particles were used, their surface was directly modified with N-(2-aminoethyl-3-aminopropyl)methyldimethoxysilane to yield SiO2-NH2, followed by the grafting of PDMS to the particles. (We note that the diameter of the silica (core) NPs is depicted as round numbers, whereas information about the corresponding average particle sizes and size distributions is available in the Supporting Information; Table S1).

Figure 1

Schematic of the NP preparation process (A). Single-reflection ATR-FTIR absorbance spectra of SiO2, SiO2-OH, SiO2-NH2, and SiO2-PDMS NPs with a silica (core) diameter of 80 nm (B). The black arrows in the FTIR spectra indicate characteristic FTIR absorbances of the (modified) NPs. Nonisothermal TGA thermograms of SiO2-NH2 and SiO2-PDMS NPs with silica (core) diameters of 20 and 80 nm (C).

Figure B shows representative FTIR absorbance spectra of the (modified) NPs. The remaining ethoxy groups following the Stöber reaction of tetraethyl orthosilicate (TEOS) can clearly be observed in the FTIR spectra of the SiO2 particles, that is, the CH2/CH3 bending absorbance band at 1452 cm–1 and the CH2/CH3 absorbance band at 2980 cm–1.[49] Following hydrolysis to obtain SiO2 NPs with surface −OH functionalities (SiO2-OH), these absorbance bands disappeared, which indicates quantitative hydrolysis of the ethoxy groups.[50] The reappearance of the bands at 2980, 1450, and 1380 cm–1 in the FTIR spectrum of amino-functionalized NPs (SiO2-NH2) indicates the successful surface modification with NH2 groups. This indication is strengthened by the fact that the SiO2-NH2 NPs resulted in a positive ninhydrin color test,[51]confirming the presence of NH2 groups on these particles. The absorption bands for CH3 stretching at 2967 cm–1 and for C–H bending at 1263 cm–1 confirm the successful grafting of PDMS to the NPs.[52]

We employed TGA analyses to determine the amount of grafted polymers. Figure C shows an example of the weight loss versus temperature curves for nonisothermal TGA measurements of SiO2-NH2 and PDMS-grafted NPs, with silica (core) diameters of 20 and 80 nm, respectively. The weight percentage of PDMS bound to the NPs was calculated from the TGA charts (see Table S2). The results show that the amount of grafted PDMS increases from ∼3.1 to ∼24.2 wt % with a decrease in the NP diameter from 120 to 12 nm. This is ascribed to the increased specific surface area for the smaller particles. On the basis of the TGA results, the molar mass of the grafted PDMS chains used (i.e., 1000 g mol–1), and the surface area of the nanoparticles (e.g., 33 m2 g–1 for 80 nm nanoparticles), the values of PDMS grafting densities were estimated to be approximately ∼0.9 chains nm–2 for particles with a diameter between 12 and 120 nm (see Table S2). Thus, the variations in silica NP size and thus surface curvature did not affect the PDMS grafting densities.

TEM was used to confirm the core–shell structure of the hybrid NPs. Figure shows TEM images of bare and PDMS-grafted NPs with silica core diameters of 20 and 80 nm, respectively. A clear PDMS shell structure around the NPs can be observed (see Figure C,D). From the TEM images, the shell thickness value was estimated to be in the range of 6.0 ± 1.3 nm. The NPs obtained were subsequently used as heterogeneous nucleation agents for PMMA nanocomposite foaming.

Figure 2

TEM images of SiO2-OH NPs with diameters of 20 nm (A) and 80 nm (B) as well as SiO2-PDMS NPs with silica core diameters of 20 nm (C) and 80 nm (D). The scale bars correspond to 50 nm.

Nanocomposite Foams

Prior to foaming, the NPs were melt-blended to PMMA and pressed to films with a thickness of typically 200 μm. (As already mentioned, for comparison, we kept the volume number density of the particles with different diameters constant at the value of 2.3 × 1013 particles cm–3.)

PMMA nanocomposites with bare and core–shell NPs were foamed after saturation with CO2 at 55 bar. Figure shows SEM images of cross-sectioned PMMA foams containing 20 and 80 nm diameter particles, respectively, after 180 s of foaming. From Figure , it is obvious that the incorporation of PDMS-grafted NPs can significantly decrease the cell size and increase the cell density compared to those of untreated silica (compare Figure B with Figure D). For quantitative comparison, the values of the cell size and cell density of representative PMMA foams were determined and are shown in Figure as a function of the NP core diameter.

Figure 3

SEM images of cross-sectioned PMMA foams containing SiO2-OH NPs with diameters of 20 nm (A) and 80 nm (B) as well as PMMA foams containing SiO2-PDMS NPs with silica core diameters of 20 nm (C) and 80 nm (D). The scale bars correspond to 1 μm. The saturation pressure, foaming temperature, and foaming time were 55 bar, 40 °C, and 180 s, respectively.

Figure 4

Cell size (A), cell density (B), and nucleation efficiency (C) of PMMA nanocomposite foams containing SiO2-OH and SiO2-PDMS NPs as a function of the silica (core) diameter. (D) Cross-sectional SEM image of a PMMA foam specimen containing PDMS-grafted nanoparticles with a silica core diameter of 80 nm (foamed for 180 s). The scale bar represents 200 nm. (Note: The error bars for the measurements involving bare silica in (B) and (C) are too small to be seen.).

For comparison, PMMA foams (obtained under the same foaming conditions) without added nucleating agents featured cell size and cell density values of approximately 13 μm and 3 × 108 cells cm–3, respectively. Thus, the addition of the NP nucleating agents used here has a substantial effect on the foam morphology. Additionally, as it is obvious from Figure A,B, the cell size and cell size distribution decrease, whereas the cell density increases upon the increase of the nanoparticle size. For example, the cell size and cell density with 120 nm bare silica NPs are ∼810 nm and 2.1 × 1012 cells cm–3, respectively, which is a significant enhancement compared to that in the foam obtained using 12 nm bare NPs. After the incorporation of surface-grafted core–shell NPs, the cell sizes are further decreased and the cell densities are significantly increased compared to those of the foams featuring bare silica only. For instance, for PMMA foams nucleated by 120 nm SiO2-PDMS NPs, the cell size decreased to ∼410 nm and the cell density increased to 1.09 × 1013 cells cm–3.

Strikingly, there is a sharp and unexpected increase in the cell density with the increasing size of SiO2-PDMS NPs starting at a particle diameter of ∼40 nm and reaching a plateau value at ∼80 nm. This effect will be discussed later.

The nucleation efficiencies of the nanoparticles were calculated as the ratio of the number of cells per cm3 of the unfoamed polymer to the number of nanoparticles per cm3 of the unfoamed polymer (i.e., 2.3 × 1013; see also the Materials and Methods section ). (We consider here unfoamed material, as the cell number considered here does not include the foam expansion factor.) It is assumed that (i) there is no cell coalescence during foaming and (ii) that every particle provides one potential nucleation site. However, we note that the number of nucleation sites per particle is not limited to 1. In principle, there are no physical restrictions that prevent the occurrence of more than one nucleation event per particle, that is, nucleation efficiencies exceeding unity are possible.

The nucleation efficiency of NPs with a PDMS shell is significantly higher compared to that of the bare silica. For instance, a nucleation efficiency of 0.47 was obtained for the PDMS-decorated silica with a core diameter of 80 nm, which is 12-fold higher compared to the value observed for the corresponding untreated NPs (which had a nucleation efficiency of ∼0.04). The SEM images shown in Figure D reveal that every cell cross section contains approximately one particle. We note that this number was confirmed by examining both halves of cross-sectioned PMMA foams with SEM. If we assume that on average every cell was cut in half this would correspond to two particles to nucleate one foam cell. This is in excellent agreement with the determined nucleation efficiency of ∼0.5 as determined by image analysis.

We note that our NPs perform significantly better when[AQ6] the nucleation values were compared to typical values, that is < 0.01, for other nucleating agents for example nanoclay,[12,22] nanotubes,[53] and CO2-philic polyionic liquid-grafted particles.[34] Direct comparison of nucleation efficiencies is not a trivial task because efficiency values also depend on the choice of the foam matrix, as well as on the foaming process parameters. Nevertheless, we ascribe the increase in cell density and high nucleation efficiency observed in our experiments to (i) the good NP dispersion in the polymer matrix (see Figure S2), (ii) the low surface energy of the PDMS shell, which reduces the nucleation energy barrier, and (iii) the higher local CO2 concentration in the PDMS shell (∼75 wt %)[54] compared to that in the PMMA (∼18 wt %) matrix.[55] The higher CO2 concentration in the PDMS shell ensures that upon decreasing the pressure and increasing the temperature during foaming the amount of CO2 available for foaming is higher closer to the heterogeneous nucleation sites compared to that in the bulk of the matrix.[13] This is expected to result in a higher nucleation rate at the particle interphases. In addition, it was reported that due to polymer phase separation the nucleation energy barrier for cells nucleated at the interphase is reduced, as well.[56,57]

We attempted to prepare hybrid NPs with a higher PDMS grafting length to enhance the CO2 adsorption in the nucleating interphase. Upon increasing the grafting length by using 5000 g mol–1 PDMS, NPs with a core diameter of 80 nm had similar grafting percentages compared to those of the shorter PDMS grafts. For this size of core–shell NPs, similar nucleation efficiencies were obtained. On the contrary, the smallest particles (diameters below 40 nm) had a significant increase in grafting percentages for the longer PDMS chains. Surprisingly, this did not result in a significant increase in the cell nucleation efficiency for these NPs. This is ascribed to the inefficient cell nucleation of NPs with (core) diameters below 40 nm as we will later discuss.

To further elucidate the cell nucleation process at the interface of the nanoparticles, we foamed PMMA over a very short period of time, that is, 0.3 s. (We note that this was the shortest foaming time we could experimentally achieve.) Figure shows cross-sectional SEM images of PMMA foam cells containing bare and PDMS-grafted silica with core diameters of 20 and 80 nm, respectively, after foaming for 0.3 s. From Figure , it is clear that these foams have on average a smaller cell size and a thicker cell wall compared to those of the foams obtained over 180 s (see Figure ). This we attribute to the limited time for cell growth. For instance, PMMA foams containing 80 nm PDMS-grafted NPs foamed for 0.3 and 180 s have average cell sizes of approximately 290 and 430 nm, respectively. Clearly, in the foaming process, nucleation is followed by rapid cell growth. Unfortunately, the experimental limitations do not allow us to capture the cell morphology right after nucleation, that is, on a time scale faster than 0.3 s.

Figure 5

Cross-sectional SEM images of 0.3 s foamed PMMA containing SiO2-OH with diameters of 20 nm (A) and 80 nm (B) as well as SiO2-PDMS with core diameters of 20 nm (C) and 80 nm (D). The scale bars represent 1 μm. The insets are SEM/EDS images of the magnified parts, and the scale bars in these inserts represent 200 nm.

Whereas most of the reports discussing heterogeneous nucleation with spherical particles ignore the position of the nucleating particles in the final foam morphology, we actually obtained valuable information from imaging of the position of the NPs after foaming. Namely, a striking difference in the morphologies captured in Figure is the absence of NPs with 20 nm diameter at the polymer wall cell interface, whereas the 80 nm particles are clearly visible (and protruding). In addition, the 12 and 40 nm SiO2-OH and SiO2-PDMS nanoparticles were not visible at the cell wall surface either. Particles with a core diameter of 60 nm and larger at the cell wall were observed for both SiO2-OH and SiO2-PDMS NPs. This surprising effect will be discussed in the next section.

Line Tension Effects on Heterogeneous Nucleation

In this section, we turn our attention to line tension effects to elucidate the observed differences and clarify its contribution to the free energy of cell nucleation. In Figures and 7, we provide schematics of a proposed CO2-NP cell embryo and proposed steps of cell growth for different NP sizes.

Figure 6

Sketch of the cross section of a proposed CO2 embryo with radius r* in equilibrium with the CO2 swollen polymer shell on a spherical seed particle with radius R.

Figure 7

Scheme of cell nucleation and initial cell growth from nanoparticles with a diameter below 40 nm (A) and above 60 nm (B). R and r* denote the radius of nanoparticles and critical CO2 embryo, respectively. The line tension of a curved three-phase contact line acts along the tangents of the contact line circle.

Upon closer examination of a particle during nucleation, it is obvious that a three-phase contact line exists at its surface (see Figure ) and thus contributions of a line tension (τ) in the order of 10–12–10–6 N m–1 must be considered to the nucleation free energy barrier.[39,58] Following nucleation of a capped nucleus on a highly curved particle,[59] a positive line tension eventually results in the engulfment of the nanoparticle by the polymer in the foam cell walls (see Figure A). Although the frequently used classical nucleation theory for foam cell nucleation considers particle curvature effects,[60] it does not include line tension effects in the nucleation energy barrier. When considering line tension effects, the nucleation energy barrier can be written according to eq .[59,61]where ΔG* is the nucleation energy barrier, r* is the critical radius of a CO2 embryo, σ is the surface free energy between polymer and CO2, R is the nanoparticle radius, S is the surface area between the critical CO2 embryo and nanoparticle, and τ is the three-phase contact line tension.

The surface area, S, can be obtained from eq (59)Angle ⌀ (see Figure ) is given by[62]where θ is the contact angle (see Figure ).

f(m, w) is the energy reduction factor according to the classical nucleation theory[60]in whichHere, ΔP is the pressure difference between the blowing agent saturation pressure and the atmospheric pressure.[27]

Although the magnitude of line tension for numerous systems is still under debate, it is agreed that for a positive line tension particles engulf when their radius is smaller than the line tension length (i.e., L = τ/σ). Hence, the engulfment of the smaller particles (i.e., a diameter below 40 nm) by the polymer following bubble nucleation, as depicted in Figure A, is in agreement with L being approximately 20 nm, and provided that σ is ∼21 mN m–1 for the foaming conditions used,[63] we estimate that the line tension is ∼0.42 nN. The critical bubble radius for our CO2 PMMA-saturated system is on the order of 3 nm for a saturation pressure of 55 bar (see also eq ).[64] In addition, from high-resolution SEM images, the CO2 swollen polymer–particle contact angles of bare and PDMS-grafted particles with a silica core of 80 nm were determined to be ∼79 and ∼28°, respectively (see Figure S3). The lower contact angle for the 80 nm SiO2-PDMS particles compared to that of the bare NPs is ascribed to the high affinity of the grafted NPs to the CO2 phase, and it explains also the higher nucleation efficiency. (We note that here identical contact angle values are assumed for nanoparticles with the same surface chemistry.)

Figure shows the calculated nucleation energy barrier as a function of the contact angle (θ) (Figure A) and the critical radius (r*) (Figure B) according to eq , using a line tension value of ∼0.42 nN.

Figure 8

Nucleation energy barrier of the formation of a critical CO2 embryo on nanoparticles as a function of the contact angle for a line tension of 0.42 nN (solid lines) as well as without the contribution of line tension (dashed lines) (A). The critical cell nucleation radius is 3 nm. The nucleation energy barrier as a function of the critical CO2 embryo radius for a line tension of 0.42 nN and a contact angle of 28° (B).

From Figure A, it is clear that for a positive line tension of 0.42 nN the nucleation energy barrier (shown by the solid lines) is significantly increased when particles exist at the polymer gas interface (i.e., when θ is not 0 or 180°) compared to the barrier calculated according to the classical nucleation theory (shown by the dashed lines).

Of particular interest is that for the PDMS-grafted NPs (θ is 28°) the nucleation energy is significantly increased by the contribution of line tension for the 12, 20, and 40 nm particles compared to that for their larger counterparts (diameter > 60 nm). Overall, the bare silica particles (θ is 79°) have a higher nucleation energy barrier compared to that of the grafted ones. Interestingly, for the smaller bare silica nanoparticles, the effect of line tension on the nucleation barrier is less pronounced. In addition, the larger bare NPs (>60 nm) have nearly identical nucleation energy barriers. These results corroborate the nucleation efficiency values presented in Figure , which show a sudden increase for particles larger than 40 nm when the contact angle for nucleation is low, that is, for the particles with a PDMS shell, whereas for the bare silica particles, there is a more steady increase of the nucleation efficiency. Interesting to mention here is that CO2-philic block copolymer-based heterogeneous phases are considered as promising nucleation agents, as well.[8,65,66] In fact, Rodriguez-Perez and co-workers[66] reported a nucleation efficiency close to unity for poly(methyl methacrylate)-co-poly(butyl acrylate)-co-poly(methyl methacrylate) block copolymer (BCP) domains in PMMA. This high nucleation efficiency could be explained by the fact that depending on the nucleation point in the phase-separated morphologies of the BCPs, these block copolymer domains do not experience a line tension.

The nucleation efficiency values and the results presented in Figure A demonstrate that particle size is an important parameter to control and optimize the foaming process in the presence of nanoparticles employed as nucleating agents.

A frequently used strategy to further increase the foam cell nucleation efficiency is to increase the CO2 saturation pressure, resulting in (i) a decrease of the surface energy of the CO2 swollen PMMA[63] and (ii) an increase in the pressure drop, overall leading to a decreased critical bubble radius for foam cell nucleation (see eq ). In addition, the decreased surface energy at higher CO2 saturation pressures is expected to result in an increased line tension length. In fact, following CO2 saturation at 300 bar and subsequent foaming for 0.3 s at 40 °C, we observed nearly complete engulfment of the 60 and 80 nm bare and PDMS-grafted NPs (see Figure S4), indicating an increased line tension length indeed. This is in line with the observed decrease in nucleation efficiency to ≪0.1, for particles with a silica (core) diameter below 80 nm under foaming conditions utilizing a CO2 saturation pressure of 300 bar (data not shown).

To what extent line tension contributed to the reduced nucleation efficiency at these foaming conditions must still be elucidated. The critical bubble radius for PMMA films saturated with 300 bar CO2 is reduced to values below 1 nm.[63] This means that for these smaller capped nuclei on the surface of the nanoparticles (diameter > 12 nm) the three-phase contact line is diminished and as a consequence its contribution to the heterogeneous nucleation energy barrier is reduced, as well (see Figure B). In addition, the higher the pressure drop, the more favorable homogenous nucleation is compared with the heterogeneous nucleation process.[14] Interestingly, we observed evidence for homogenous nucleation in parts of the cell walls of PMMA foams prepared with a saturation pressure of 300 bar, which is in agreement with the reduced nucleation efficiency observed, as well. This means that following foaming from higher saturation pressures the resulting smaller critical bubble radius decreases the energy penalty attributed to line tension for nucleation, while homogenous nucleation becomes more favorable.[59] This limits the foam processing window where particles are effective as nucleation agents. Under conditions when NPs are effective (i.e., for lower pressure drops), relatively large particles are needed compared with the targeted sub-micrometer foam cell sizes to reduce the effect of particle curvature and line tension on foam cell nucleation. This means that new strategies and particle designs must be developed that increase the nucleation efficiency and result in foaming of nanocellular PMMA foams with cell densities exceeding 1015 cells cm–3.

Conclusions

PDMS-decorated and bare silica NPs with (core) diameters between 12 and 120 nm were exploited as heterogeneous nucleation sites in CO2-blown PMMA nanocellular batch foaming. NPs grafted with a ∼6 nm thick PDMS shell were found to be more efficient as nucleation agents compared with their bare counterparts. The highest nucleation efficiency obtained was ∼0.5, and the optimum core diameter of PDMS-grafted NPs for cell nucleation was around 80 nm. The complete engulfment of particles with a (core) diameter below 40 nm by the polymer foam cell wall in the cell wall corresponds to a line tension of ∼0.42 nN. It is shown that line tensions of this order of magnitude result in a significant increase in the free energy barrier of heterogeneous nucleation. As a consequence, the smallest NPs used were not as effective as expected. At higher CO2 saturation pressures (300 bar), the line tension length increased such that particles up to 80 nm were nearly entirely engulfed by the polymer foam cell wall. The smaller critical bubble radii for these foaming conditions result in a significantly decreased contribution of line tension to the nucleation free energy. Thus, the observed decrease in the nucleation efficiency for these foaming conditions is ascribed to homogenous nucleation becoming more favorable. Overall, it is shown that line tension contributes to the nucleation energy barrier in foaming of viscoelastic media and that as a consequence it affects the nucleation efficiency of highly curved NPs in the foam processing window where heterogeneous nucleation is favorable. The deeper fundamental insight obtained emphasizes the need for the development of new foaming strategies and particle designs that are expected to further enhance the nucleation efficiency of NPs in polymer nanocellular foaming.